Definition of Differentiation
Sarah Miller
5 min read
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Study Guide Overview
This study guide covers instantaneous rate of change, focusing on its definition as the slope of a graph at a specific point. It explains how to calculate it using limits and its relationship to the derivative. Examples, practice questions, and a glossary of key terms (including average rate of change) are provided.
#Instantaneous Rate of Change
#Table of Contents
- What is the Instantaneous Rate of Change?
- Finding the Instantaneous Rate of Change
- Worked Example
- Practice Questions
- Glossary
- Summary and Key Takeaways
#What is the Instantaneous Rate of Change?
The instantaneous rate of change is the slope of a graph at a specific point, rather than between two points.
The instantaneous rate of change at a point on a function is essentially the derivative at that point. It measures how the function value changes as the input changes infinitesimally.
#Finding the Instantaneous Rate of Change
Consider the graph of a function with two points on the graph, and :
#Average Rate of Change
Using the labeling on the left:
- The average rate of change from to can be written as:
Using the labeling on the right:
- T...
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